Magic of infinity

Algebra Level 3

yy is real number

a2+a+a2+a+a2+a+a2+a+a2+a=y \sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a+\sqrt { { a }^{ 2 }+a\dots } } } } } =y

Find y2y^{2} when a2=10000a^{ 2 } = 10000

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